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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 8th 2010

    I added some simpler motivation in terms of the basic example to the beginning of distributive law.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeOct 11th 2010
    Thanks, nice.
    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 12th 2010

    Yes, nice. Rings make an obvious choice to illustrate a distributive law between monads. Then we’re introduced to the scary thought that there’s a whole 2-category of such laws. Could this be illustrated by a surprising example or two of a distributive law, perhaps something one would never have thought to be such a law?

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeOct 12th 2010

    one would never have thought to be such a law

    The level of difficulty in fullfilling this task depends on who is "one" who never thought...

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeOct 12th 2010

    There’s definitely a gap between the first two sections of this page which someone who has some time on their hands should fill. (-:

    • CommentRowNumber6.
    • CommentAuthorFinnLawler
    • CommentTimeOct 12th 2010

    a surprising example

    I for one was quite tickled to find out that factorization systems are distributive laws between categories taken as monads in Span(Set). That might be a good non-obvious example.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 13th 2010

    Good. I’ve put that example in.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeOct 14th 2010

    It’s not quite true as stated, though – ordinary distributive laws in Span(Set) only give you “strict” factorization systems. I corrected it.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2012

    I keep pointing to “distributive law” whenever I mention something distributive. Now looking back at the entry to see what it actually says, I notice that many of the common “distributivities” were not really mentioned. I added a quick pointer to distributive category and to tensor products distributing over direct sums. But this needs to be better incorporated into the entry, eventually.

    • CommentRowNumber10.
    • CommentAuthorPaoloPerrone
    • CommentTimeSep 27th 2019

    Added explicit diagrams.

    diff, v26, current

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